Part II: The evaluation of distinguishing standards criteria by using TOPSIS method

4.3 Part II: The evaluation of distinguishing standards criteria by using TOPSIS method

Multi-Attribute Decision Making (MADM) approaches are formal methods used to organize the information and evaluate decisions in areas with multiple conflicting objectives. These methods can help decision-makers understand the results of comprehensive assessments and use the results in a systematic way. MADM methods are widely used in many fields of research from which different approaches have been proposed by various researchers (Wang et al. 2009).

TOPSIS method was originally developed by Hwang and Yoon in 1981. According to this technique, the best alternative has the shortest distance from the positive ideal solution (PIS) and the longest distance from the negative ideal solution (NIS). The positive ideal solution is one that has the maximum benefit and minimum cost and the negative ideal solution is that with the

minimum benefit and maximum cost. In TOPSIS method, in addition to taking the distance of alternative Ai from the ideal point, its distance from the negative ideal point is also considered. This means that the chosen alternative must have the shortest distance from the ideal solution while having the longest distance from the negative ideal solution. As its name implies, the ideal solution is the best one in every respect which is virtually not possible and one will try to approach it (Moraveji and Mohammadipour, 2009).

In this part of the article, TOPSIS analysis approach used in most engineering problems is utilized to evaluate, analyze and compare the result. The standard prioritization and the distinction criteria in project management have been achieved using the expert judgments in this area and by analysis parameter assessment TOPSIS software. The standards and criteria have been categorized into four groups and eight criteria presented in the table 5.

Table 5: Prioritization of standards and standard criteria for project management

Attribute Criterion

Attribute Standard

C1 1. The distinction between project management and competency

standards A1

PMBOK2008

C2 2. Application in various projects

A2 PRINCE2

C3 3. Provide competency with respect to the definitions accepted in

the world A3

0PM

C4 4. Compliance of knowledge competency with the standards

A4 ISO-10006

C5 5. Compliance of performance competency with the standards

C6 6. Levels of examined competency

C7 7. Type of admission

C8 8. Evolution of behavioral competence

4.3.1 Create a decision matrix

A matrix will be drawn at this step having alternatives in its rows, attributes in its columns and the weight of each attributes

in the last row, and the intersection of rows and columns gives the importance of each respondent for any of the alternatives with respect to the corresponding attributes (table 6).

Table 6: Decision matrix (N)

C^Rn

… C^R2

C^R1

index

criteria

r^R1n

… r^R12

r^R11

A^R1

r^R2n

… r^R22

r^R21

A^R2









r^Rmn

… r^Rm2

r^Rm1

A^Rm

W^Rn

… W^R2

W^R1

W^Rj

rij is the score of i th alternative in j th attribute and wj is the weight of j th attribute.

The following algorithm provides the relations of standards and criteria in TOPSIS pattern of the project.

Note that the decision matrix (Table 7) is the arithmetic mean of all expert judgments.

A1-A4: standards, C1-C8: criteria

Table 7: Decision Matrix (N)

C1 C2 C3 C4 C5 C6 C7 C8

Index type Positive Positive Positive Positive Positive Positive Positive Positive

A1 6.5 5.7 7.7 6.5 7.5 8.935 6.5 6.5

A2 5.5 5.5 5.9 6.5 7.5 7.25 5.3 5

A3 6.5 5.4 6.8 6.54 7.5 7 5.35 4.88

A4 6.5 6.25 6.27 5.5 7.5 6.5 5.5 6

4.3.2 Normalize the decision matrix

In order to be comparable, the decision matrix is converted to the

normalized (incommensurable) matrix using Eq. (2).

∑

=

=

m i

ij ij ij

r n r

1

2 (2)

Table 8 shows the incommensurable matrix:

Table 8: Incommensurable matrix (N1)

C1 C2 C3 C4 C5 C6 C7 C8

A1 0.334 0.298 0.361 0.34 0.353 0.452 0.32 0.345

A2 0.283 0.287 0.278 0.34 0.353 0.366 0.261 0.266

A3 0.334 0.282 0.323 0.34 0.353 0.354 0.264 0.259

A4 0.334 0.326 0.32 0.288 0.353 0.329 0.271 0.319

4.3.3 Obtain the incommensurable weighted matrix

To obtain the incommensurable weighted matrix (V), the incommensurable matrix (obtained from the second step) is multiplied by the square matrix (wn×n) whose main diagonal elements are weights of attributes and other elements are zero.

n

w

n

N

V =

₁

×

_× ⁽³⁾

Table 9 shows the in commensurable weighted matrix.

Table 9: Incommensurable weighted matrix (V)

C1 C2 C3 C4 C5 C6 C7 C8

A1 0.024 0.021 0.026 0.024 0.025 0.032 0.024 0.025

A2 0.02 0.02 0.02 0.024 0.025 0.026 0.019 0.019

A3 0.024 0.02 0.023 0.024 0.025 0.025 0.02 0.019

A4 0.024 0.023 0.023 0.02 0.025 0.023 0.02 0.023

4.3.4 Determine the positive and negative ideal factors At this step, such options should be identified that are considered by the respondents as most important and least important factors.

In other words, for positive indices, the positive and negative ideals are the largest and smallest v value, respectively; also, for

negative indices, the positive and negative ideals are the smallest and largest v value, respectively. This is expressed by Eqs (3) and (4).

Positive ideal

{

^{+ + +}

}

+

=

 



 

  =



 



 ∈ ′

 

 



 ∈

=

_n

i ij i

ij

j J V j J i m V V V

V

A max , min | 1 , 2 , ...,

₁

,

₂

, ...,

⁽⁴⁾

Negative ideal

{

^{− − −}

}

−

=

 



 

  =



 



 ∈ ′

 

 



 ∈

=

_n

i ij i

ij

j J V j J i m V V V

V

A min , max | 1 , 2 , ...,

₁

,

₂

, ...,

(5)

In this relations, J is positive index and

J ′

is negative index.

Table 10 shows the positive and negative ideals. The performance criteria obtained the least positive ideal and the

‘number and type of involved organizations’ and ‘type of competence’ criteria obtained the least negative ideals (figure 2).

Fig. 2: TOPSIS network diagram for standard methods and criteria in project management Table 10: Positive and negative ideals of each index

Criterion Positive negative

C1 0.029 0.02

C2 0.028 0.02

C3 0.026 0.02

C4 0.028 0.02

C5 0.025 0.022

C6 0.032 0.02

C7 0.031 0.019

C8 0.029 0.019

4.3.5 Calculate the distance from the positive and negative ideals

At this step, the distance of each option from positive and negative ideals is determined according to Eqs (6) and (7).

The distance of ith option from the positive ideal is

( ^{V V} ) ^{i m}

d

n

j

j ij

i

; 1 , 2 , ...,

1

2

=

−

= ∑

=

+

+ (6)

The distance of i th option from the negative ideal is

( ^{V V} ) ^{i m}

d

n

j

j ij

i

; 1 , 2 , ...,

1

2

=

−

= ∑

=

−

− (7)

4.3.6 Calculate the closeness level (CL) of each factor to the positive and negative ideals

At this step, the closeness level of each option to the positive and negative idealsis obtained by Eq. (8).

+

−

−

= +

i i

i

i

d d

CL d

(8)

Table 11 shows the CL values for each option.

4.3.7 Step Seven: Rank the options

At this step, the options are ranked based on CL values; in other words, any option having a higher CL will earn a better ranking.

Table 11 shows the ranking of options.

Table 11: Ranking of Options

Rank CL The ideal distance from negative The ideal distance from Positive choices

1 0.48 0.02 0.022 A1

2 0.425 0.019 0.031 A2

3 0.33 0.016 0.027 A3

4 0.295 0.014 0.022 A4

The results obtained from the ranking of options with TOPSIS technique indicate that the PMBOK standard in this country has taken a high priority over other options.

5. Solutions

If the weakness and distance from the requirements of project management body of knowledge are based on process plans related to the cases within each of the nine areas of project management, continuing and going through a recovery process

and performing periodic audit could be done to amend the procedure and reduce the distance to the standard. The organizational project management is the systematic management of projects in order to achieve the strategic goals of the organization. This concept that there is a direct relationship between the skill and ability of an organization to manage its projects and its success in implementing strategies, is the fundamental and theoretical basis of organizational maturity and organizational project management.

Although each of the projects may arise short-term, or at most, medium-term issues for the organization, the project management in an organization can create a strategic competitive advantage for the organization. The successful implementation of project management in the organization will lead to selecting the projects proportional to the organization's goals, properly allocating resources of project organizations, successfully completing the projects, and ultimately, the success of organization. An organizational maturity model represents a conceptual framework with relevant components to show the degree of maturity of the organization in the respective field. For some models, the process of transforming the organization from lower levels to higher ones may be described. The model may also be step by step (discrete) or continuous. Project management, time management, cost management and quality together can provide a complete view of the status of project management in an organization that also identify the susceptible areas of possible improvements. Accordingly, the following steps are recommended to be followed in the studied organization:

In document QUAERE 2017 (Stránka 65-68)